Pat the chicken breast dry with a paper towel, then cut into bite-sized pieces and toss in a bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
In a small bowl, whisk together the honey, tamari, minced garlic, and grated ginger to create the stir-fry sauce.
Heat the sesame oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the chicken to the pan in a single layer and sear for 3-4 minutes per side until golden brown and cooked through, then transfer the chicken to a plate.
In the same skillet, add the broccoli florets and sliced bell peppers with 1 tablespoon of water; cover with a lid for 2 minutes to steam until the vegetables are vibrant and crisp-tender.
Remove the lid, return the chicken to the pan, and pour the honey-garlic sauce over the mixture.
Toss everything together for 1-2 minutes until the sauce bubbles and thickens into a glossy glaze that coats the chicken and vegetables.
Serve the stir-fry immediately over the warm, cooked brown rice.